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Mathematics First Practice Test A,B & C Mental Maths Mark scheme
Introduction
This booklet contains the mark schemes for the lower tier test (test C) and the
higher tiers tests (tests A and B). The pupil answer sheets will be marked by
external markers who will follow the mark schemes in this booklet, which are
provided here for teachers’ reference.
General guidance for markers
Please note that pupils should not be penalised if they record any information
given in the question or show their working. Ignore any annotation, even if in the
answer space, and mark only the answer. Accept an unambiguous answer written
in the stimulus box, or elsewhere on the page, but clearly attributable to the
relevant question.
General guidance for marking the written tests also applies to marking the mental
mathematics tests. In addition, please apply the following principles unless specific
instructions to the contrary are given in the mark scheme:
accept responses in words and/or figures,
eg 7 point 3, 4 hundred
accept any unambiguous indication of the correct response from a given list,
eg circling, ticking, underlining
accept unambiguous misspellings
accept units that have been correctly converted to a different unit, provided the
new unit is indicated. Where units have been given on the answer sheet, do not
penalise pupils for writing the units again
accept responses with commas as spacers,
eg 50,000
but do not accept a point used as a spacer,
eg 50.000
3
10
14 15 16 10
11
11
£
49
train bus
adult £2.00 £1.20
child £1.00 40p
12
12
£
13
25th July 13
men
women
14
= 25 people
14
15 3 3
2
15
16
°
N
W E
S
16
1 Add sixty-seven and fourteen.
2 How many sides does an octagon have?
3 Double nineteen.
4 Round four thousand two hundred and sixty-six to the nearest ten.
5 Multiply six by seven.
6 Look at the expression. Write it as simply as possible.
7 Write one quarter as a decimal.
8 What is nought point eight multiplied by five?
9 Look at the numbers on your answer sheet.
Put a ring round the largest number.
10 Add together fourteen, fifteen and sixteen.
11 Look at the coins.
How much money is shown altogether?
12 The table shows the price of a journey by train or bus.
How much will it cost two adults and one child to make the journey by bus?
13 John went to France on the twenty-fifth of July and returned
exactly one week later.
On what date did John return?
14 The chart shows the number of men and women who work at a factory.
One symbol represents twenty-five people.
How many more men than women work at the factory?
15 Subtract three from three squared.
16 Sam is facing North. He turns clockwise to face North-East.
Through how many degrees does he turn?
4 Lower tier test C questions
‘Now we are ready to start the test.
For the first group of questions you will have 5 seconds to work out each answer
and write it down.’
Pupil answer sheet
Mental mathematics Test C
First name
Last name
School
Total marks
Time: 10 seconds
9 2010 2001 2100
2110 2101 9
Practice question
‘For the next group of questions you will have 10 seconds to work out each answer
and write it down.’
Time: 5 seconds
1 67 14
1
2
2
3
19 3
4
4266 4
5
6 7 5
6
7k – 4 k 6
7 1
4
7
8
0.8 5 8
‘Now turn over your answer sheet.’
70°
17 Look at the temperature shown on the thermometer.
The temperature drops by five degrees Celsius. What is the new temperature?
18 Eight kilometres is about five miles.
About how many miles is twenty-four kilometres?
19 Look at the triangle drawn on the grid.
Write the coordinates of the point marked A.
20 What is the square root of eighty-one?
21 Look at the expression. I subtract three from the expression.
Write the new expression as simply as possible.
24
sleeping
eating
working
0 2 4 6 8 10
Time ( hours )
24
25
6cm 6 cm
8cm
25
cm
19 y
2
B
C 0
–2 0 2 x
– 2 A
19 ( , )
20
√81 20
28 B
C
450 g 950 g
28
g
22
3 tins for 99p
22
£
22 Your answer sheet shows the cost of three tins of cat food.
How much would six of these tins cost?
23 I am thinking of a number.
The number can be divided by three with no remainder.
It can also be divided by four with no remainder.
What could my number be?
24 The bar chart shows how Pete spent some of his day.
How many more hours did he spend sleeping than working?
25 Look at the triangle and the square.
The perimeter of the triangle is the same as the perimeter of the square.
What is the side length of the square?
26 Look at the sequence of triangular numbers: one, three, six, ten, fifteen.
What is the next number in the sequence?
27 Ben has one red marble, one green marble and three blue marbles in his pocket.
He is going to take one of the marbles out of his pocket without looking.
What is the probability it will be green?
28 Look at the information on your answer sheet.
The total mass of the three boxes is two kilograms.
What is the mass of box C?
29 Twenty-nine multiplied by thirty-four is nine hundred and eighty-six.
What is nought point two nine multiplied by thirty-four?
30 Look at the diagram. Work out the size of angle a.
5
Time: 10 seconds continued Time: 15 seconds continued
17 °C
–6 –4 –2 0 2 4
17
°C
18
8 km 5 miles
18
miles
‘For the next group of questions you will have 15 seconds to work out each answer
and write it down.’
26 1, 3, 6, 10, 15, 26
27
1 red 1 green 3 blue
27
A
21 5b + 3 21
Time: 15 seconds 29 29 × 34 = 986
0.29 × 34 =
29
30
° a
23 1 23 30
‘Put your pens down. The test is finished.’
Key stage 3 mathematics 2006
Mental mathematics higher tiers Test A
Test A Mark scheme
Mental mathematics lower tier Test C
Time: 10 seconds
9
2010 2001 2100
Test C Mark scheme
10 45
2110 2101
11 £ 1.13
12 £ 2.80
Time: 5 seconds
1 81
2 8
3 38
13 1st August Accept any
unambiguous or commonly used
indication of the date,
eg 1 Aug, 1/8 or
8/1 [US notation]
Ignore years given
4 4270 14 75
5 42
6 3k 15 6
7 0.25 Accept
equivalent decimals
Do not accept
equivalent fractions
16 45 ° Accept 45 + any
multiple of 360
8 4 (.0)
6
Time: 10 seconds continued Time: 15 seconds continued
17 –3 °C 24 3
18 14.9 answer 15.1 miles
19 (1, –2) 25 5 cm
26 21
20 9 Accept –9 with 9
or alone
Accept embedded values
eg 9 × 9
27 1
5
Accept equivalent
probabilities
28 600 g
21 5b
Time: 15 seconds 22 £ 1.98
29 9.86 Accept equivalent
fractions or decimals
23 Any multiple of 12
Accept zero or negative multiples of 12
30 100 °
7
8
300 8
9
9
2 cm
99
10
40 50 10
11
55°
p 25°
11
°
12
a = 5b – 4 12
13
20% 6 13
14
miles
40 mph 14
15
20 15
16 3( a – 5 )
16
17
5.7 17
1 How many sixes are there in forty-two?
2 Look at the numbers on your answer sheet.
Write down the number that is the mode.
3 Look at the expression. Write it as simply as possible.
4 Subtract nought point one from four.
5 What number is eight more than minus two?
6 Look at the number on your answer sheet. Round it to one decimal place.
7 What is the gradient of the line with equation y equals three x plus two?
8 There are three hundred people at a concert.
One hundred and fifty-five of them are male. How many are female?
9 Look at the shaded triangle drawn on a centimetre square grid.
What is the area of the triangle?
10 Write down the multiple of twelve between forty and fifty.
11 Look at the triangle. Work out the size of angle p.
12 Look at the equation on your answer sheet.
When b is three, what is the value of a?
13 Twenty per cent of a number is six. What is the number?
14 I travel at a constant speed of forty miles per hour.
How far do I travel in two and a half hours?
15 On average I take twenty breaths in one minute.
How many breaths is that in one hour?
16 Look at the expression. Multiply out the brackets.
17 Look at the number on your answer sheet. Halve it.
8
Higher tiers test A questions
‘Now we are ready to start the test.
For the first group of questions you will have 5 seconds to work out each answer
and write it down.’
Pupil answer sheet
Mental mathematics Test A
First name
Last name
School
Total marks
Time: 5 seconds continued
7 y = 3x + 2 7
Time: 10 seconds
‘For the next group of questions you will have 10 seconds to work out each answer
and write it down.’
Practice question
Time: 5 seconds
1
42 1
2 8 4 7
4 9
2
3
4b + 5b 3
6
4.875 6
4
0.1 4 4
5
–2 5
18 In a bag, there are only red, green and blue balls.
Complete the table to show the probability of taking a blue ball.
19 In a sale, the price of a notebook is decreased by ten per cent.
What is the new price if the old price was one pound twenty?
20 Look at the expression. Write down the value of the expression when m is six.
25
2cm
a cm 10 cm
25
cm
Colour Probability
red 0.4
green 0.3
blue
Televisions Frequency
0 2
1 10
2 10
3 8
26
26
28 23
0.3 4
28
29
3
4
29
24
Yes No
24
people
30 82
30
21 One of the shapes on your answer sheet is the net of a cuboid.
Put a ring round the correct shape.
22 Twenty multiplied by thirty-eight is seven hundred and sixty.
What is twenty-one multiplied by thirty-eight?
23 Look at the square grid.
Shade one more square to give a shape with rotation symmetry of order two.
24 Thirty-two people were asked if they travelled to work by bus one morning.
The pie chart shows the results. How many people said yes?
25 Look at the cuboid. It has a volume of one hundred cubic centimetres.
Work out length a.
26 The frequency table shows the number of televisions owned by thirty families.
Altogether how many televisions did they own?
27 A pyramid has five faces. How many sides does the base of the pyramid have?
28 Look at the numbers on your answer sheet. Add them.
29 Look at the rhombus. Work out its area.
30 Eight squared is the same as two to the power what?
9
Time: 10 seconds continued
18
Time: 15 seconds continued
‘For the next group of questions you will have 15 seconds to work out each answer
and write it down.’
18
19
£
£ 1.20 19
20 m3
m
20
Time: 15 seconds
21
27
5 faces 27
21
22 20 × 38 = 760
21 × 38 =
22
23
23
‘Put your pens down. The test is finished.’
1 7
13 30
6 4.9 17 2.85
Mental mathematics higher tiers Test A
Test A Mark scheme
Time: 5 seconds continued 7 3
Time: 10 seconds 8 145
9 44
1 2
Accept equivalent
2 cm
Fractions or decimals
10 48
11 100 °
Time: 5 seconds
Accept embedded values,
eg 7 × 6
2 4 Accept value(s)
indicated in list
12 11
Do not accept
incorrect % signs
14 100 miles
3 9b
4 3.9
5 6
Accept equivalent
fractions or decimals
15 1200
16 3a – 15 Accept
unconventional notation,
eg 3 × a – 15
Do not accept incomplete processing,
eg 3 × a – 3 × 5
Do not accept equivalent
fractions or decimals
Accept equivalent
fractions or decimals 10
Time: 10 seconds continued Time: 15 seconds continued
28 3.05
30 6
18 0.3 Accept equivalent
probabilities 25 5 cm
19 £ 1.08 20 36 Do not accept
incomplete processing,
eg 216 6
26 54
Time: 15 seconds
21
27 4
22 798
Accept equivalent
fractions or decimals
29 24 Ignore any
units given
23
24 12 people
Accept embedded values,
eg 26
11
7
4 C
3
2
1 A B
0 0 1 2 3 4
7
( , )
99
8 1
0 2
8
9
£
£ 3.60 9
10
mm
10 cm 10
11
2.9 11
12
°
a
12
13
5 2
13
14
148 14
1 Multiply six by six.
2 I start at four point seven and count on in equal steps: four point seven, four
point eight, four point nine.
Write down the next two numbers in the sequence.
3 Double the expression on your answer sheet.
4 Write seven-hundredths as a decimal.
5 Look at the scatter graph. It shows a type of correlation.
Put a ring round the word that describes the type of correlation it shows.
6 Write ten out of twenty-five as a percentage.
7 Look at the triangle drawn on the grid.
What are the coordinates of the point marked A?
8 Look at the scale.
About what value is the arrow pointing to?
9 What is half of three pounds sixty?
10 How many millimetres are there in ten centimetres?
11 Double two point nine.
12 Look at the diagram. Estimate the size of angle a.
13 How many fifths are there in two?
14 What is one quarter of one hundred and forty-eight?
12
Higher tiers test B questions
‘Now we are ready to start the test.
For the first group of questions you will have 5 seconds to work out each answer
and write it down.’
Pupil answer sheet
Mental mathematics Test B
First name
Last name
School
Total marks
Time: 5 seconds continued
6
%
10 out of 25 6
Time: 10 seconds
‘For the next group of questions you will have 10 seconds to work out each answer
and write it down.’
Practice question
Time: 5 seconds
1
1
2 4.7, 4.8, 4.9, ,
2
3
4pq 3
4 7
100
4
5
‘Now turn over your answer sheet.’
None Gradient High
Positive Negative
5
15 Look at the polygon. Write down its mathematical name.
16 There are seventeen red and thirteen green apples in a bag.
I am going to take out an apple without looking.
What is the probability that the apple will be green?
17 What is the next square number after thirty-six?
18 Look at the equation. What is the value of x?
19 A square of side two centimetres is enlarged by scale factor two.
What is the area of the enlarged square?
20 Look at the expression. When x is three, what is the value of the expression?
21 A cylinder has a base area of ten square centimetres and
a volume of ninety cubic centimetres. What is the height of the cylinder?
15
15
16 17 red
13 green
16
26
5
26
5 10 15
25 100
19
2 cm Scale factor 2
19
cm2
27
£
1 : 4 : 5 27
28 39.92 × 41.06
1.98
28
22
200
150
100
50
0 M T W T F S S
day
22
days
22 The line graph shows the number of ice creams sold at a cinema in one week.
On how many days were the sales more than one hundred?
23 Think about a pyramid that has a triangular base.
How many triangular faces does it have altogether?
24 Car parking costs forty pence for every five minutes.
How much will it cost to park for one hour?
25 Look at the fractions.
Put rings round all those that are greater than three-quarters.
26 A circle has a radius of five. One of the values on your answer sheet shows its
circumference. Put a ring round the correct value.
27 A million pound lottery prize is divided in the ratio one to four to five.
How much is the smallest share of the prize?
28 Look at the calculation on your answer sheet. Write an approximate answer.
29 Four numbers have a mean of twenty-five. Three of the numbers are shown on
your answer sheet. Write down the missing number.
30 Look at the graph. Write down the equation of the line labelled A.
13
Time: 10 seconds continued Time: 15 seconds continued
23
23
24
40p for 5 minutes
24
£
25 3 4 5 5 5 6
6 7
9 10 25
17
36 17
‘For the next group of questions you will have 15 seconds to work out each answer
and write it down.’
18 21 – 3x = 9 18
20
( x + 2 )( x – 1 ) 20
21 10 cm2
90 cm3
21
cm
Time: 15 seconds 29 – 20 80 40
29
30 y A
2
0
–2 0 2 x
– 2
30
‘Put your pens down. The test is finished.’
Key stage 3 mathematics 2006
Mental mathematics higher tiers Test A
Test A Mark scheme
6 40 %
either order
11 5.8
10 100 mm
Mental mathematics higher tiers Test B
Test B Mark scheme
Time: 5 seconds continued
Do not accept equivalent
fractions or decimals
Time: 10 seconds
7 ( 0, 1 )
8 1.6 answer 1.8
Accept equivalent fractions or decimals
Time: 5 seconds
1 36
2 5(.0) and 5.1 Accept pair in
3 8 pq Do not accept
unconventional notation,
eg 8 × pq
4 0.07 Accept
equivalent decimals
Do not accept
equivalent fractions
9 £ 1.80
Do not accept
amended units
Accept equivalent
fractions or decimals 12 110 ° answer 130 °
5
None Gradient High
Positive Negative
13 10 Accept embedded values,
eg 10 5
14 37
14
Time: 10 seconds continued Time: 15 seconds continued
15 Octagon Ignore additional
description,
eg regular
23 4
24 £ 4.80
16 13
30
Accept equivalent
fractions
Accept decimals as 0.43 or
better or
percentage equivalents
25 3 4 5 5 5 6
6 7
9 10
17 49
18 4
19 16 cm2
26
5 10 15
25 100
20 10 Do not accept
incomplete processing,
eg 5 × 2
27 £ 100 000
21 9 cm
28 800 answer 840
29 0
Time: 15 seconds
22 3 days
30 y = x + 1 Accept equivalent
equations
Accept unconventional
notation,
eg y = 1x + 1
15
